Hopefully by "Red Hat" you mean Redhat Enterprise Linux - preferably a recent version (RHEL5).
Package management is like fedora only with slightly different repos.
# yum install mysql-server mysql
If you do not have a RHN account (paid support) then you'll probably have to use fedoras EPEL repos
and something like CentOS.
Did you know that there is a common misunderstanding about linux "enterprise" editions? In the proprietary world, an enterprise or "pro" edition is usually the one with additional features, advancements etc. This is the opposite way round in the free software world.